## dtan5457 one year ago If y^-3x=27, compute exactly 7^2x+1

1. dan815

y^(-3x)=27, compute exactly 7^(2x)+1?

2. dtan5457

7^(2x+1)

3. anonymous

So then you need to figure out x and then plug that x-value into $$7^{2x}+1$$ ?

4. dtan5457

the +1 is part of the exponent

5. dtan5457

and yes i believe so

6. dan815

infinite solutions

7. dtan5457

what would be the steps to attempt to solve this though

8. dan815

|dw:1443998600989:dw|

9. anonymous

OK dan can you help me for a sec

10. anonymous

How do you make the exponent of y positive without putting it over 1

11. dan815

|dw:1443999336822:dw|

12. anonymous

Ohh!! got it.

13. anonymous

wow that was dumb lol.

14. freckles

$\text{If } y^{-3x}=27, \text{ compute exactly } 7^{2x+1}$ Are we given anything else? Like are we given any restrictions on x and y?

15. dtan5457

no thats all is given

16. freckles

$y^{-3x}=27 \\ y^{3x}=\frac{1}{27} \\ y^{3x}=3^{-3} \\ \ln(y^{3x})=\ln(3^{-3}) \\ 3x \ln(y)=\ln(3^{-3}) \\ 3x \ln(y)=-3 \ln(3) \\ \text{ solve for } x \\ \text{ then replace } x \text{ in } 7^{2x+1}$

17. freckles

instructions seem weird it seems like it is looking for like a constant value

18. anonymous

$\frac{1}{y^{3x}} = 27$$y^{3x} = \frac{1}{27}$$\ln(y^{3x}) = \ln\left(\frac{1}{27}\right)$$3x\ln(y)=-\ln(27)$$\ln(y)=-\frac{\ln(27)}{3x}$$e^{\ln(y)} =e^{-\frac{\ln(27)}{3x}}$$y=e^{-\frac{\ln(y)}{3x}}$

19. anonymous

darnit, took me forever to write out in latex :\ bummer

20. freckles

but as @dan815 said it isn't

21. dtan5457

its alright ill just skip this question until my teacher can explain it tomorrow

22. dtan5457

thanks guys

23. anonymous

typo, meant to write $$\ln(27)$$ and i wrote $$ln(y)$$ lol.

24. freckles

this is question come from a book @dtan5457

25. dtan5457

no just a worksheet written by my teacher

26. freckles

would it be difficult for you to post an attachment of it here?

27. dtan5457

im not sure about that as my scanner cant be used at the moment but ill probably have a few more questions from it later

28. freckles

ok

29. dtan5457

none of the questions are directly similar but its all pre calc and some trig

30. freckles

this is prettiest I can make it $7^{\log_y(\frac{y}{9})}$ but I don't know if it matches the directions to "compute exactly"